Question 1204629
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<font color=red size=4>Answer:</font> (x,y) = (3, -5)


Explanation


I'll graph each equation to show how to get that answer.
You can use a graphing tool like Desmos or GeoGebra to quickly get the answer, but I'll show the step-by-step process by hand.


To graph each line, we plot two points.
Each point is of the form (x,y)
We select any x value we want to get its paired y value.


Plug x = 0 into the 1st equation.
y = x-8
y = 0-8
y = -8
The point (0,-8) is on the line y = x-8


Repeat for x = 1
y = x-8
y = 1-8
y = -7
The point (1,-7) is also on the line y = x-8


Plot the two points (0,-8) and (1,-7) to graph the line y = x-8.
{{{
drawing(400,400,-3,12,-12,2,
graph(400,400,-3,12,-12,2,-100,x-8),

circle(0,-8,0.05),circle(0,-8,0.07),circle(0,-8,0.09),circle(0,-8,0.11),circle(0,-8,0.13),circle(0,-8,0.15),circle(0,-8,0.17),circle(0,-8,0.19),circle(1,-7,0.05),circle(1,-7,0.07),circle(1,-7,0.09),circle(1,-7,0.11),circle(1,-7,0.13),circle(1,-7,0.15),circle(1,-7,0.17),circle(1,-7,0.19),

locate(0+0.1,-8-0.1,"(0,-8)"),
locate(1+0.1,-7-0.1,"(1,-7)")
)
}}}


Repeat similar steps for the other equation. Two points on the line y = -2x+1 are (0,1) and (1,-1)
{{{
drawing(400,400,-3,12,-6,6,
graph(400,400,-3,12,-6,6,-100,-100,-2x+1),

circle(0,1,0.05),circle(0,1,0.07),circle(0,1,0.09),circle(0,1,0.11),circle(0,1,0.13),circle(0,1,0.15),circle(0,1,0.17),circle(0,1,0.19),circle(1,-1,0.05),circle(1,-1,0.07),circle(1,-1,0.09),circle(1,-1,0.11),circle(1,-1,0.13),circle(1,-1,0.15),circle(1,-1,0.17),circle(1,-1,0.19),

locate(0+0.3,1+0.1,"(0,1)"),
locate(1+0.3,-1+0.1,"(1,-1)")
)
}}}


Let's plot the two lines together on the same xy grid.
{{{
drawing(400,400,-3,12,-9,6,
graph(400,400,-3,12,-9,6,-100,x-8,-2x+1),

circle(3,-5,0.05),circle(3,-5,0.07),circle(3,-5,0.09),circle(3,-5,0.11),circle(3,-5,0.13),circle(3,-5,0.15),circle(3,-5,0.17),circle(3,-5,0.19),

locate(3+0.3,-5+0.1,"(3,-5)")
)
}}}
y = x-8 in green
y = -2x+1 in blue
The two lines intersect at (3, -5)



Let's confirm that solution.
Plug the coordinates into the 1st equation
y = x-8
-5 = 3-8
-5 = -5
The 1st equation is confirmed.
Do the same for the 2nd equation
y = -2x+1
-5 = -2(3)+1
-5 = -6+1
-5 = -5
Both equations have been confirmed true.


More practice with graphing a system of linear equations
<a href="https://www.algebra.com/algebra/homework/Percentage-and-ratio-word-problems/Percentage-and-ratio-word-problems.faq.question.1204488.html">https://www.algebra.com/algebra/homework/Percentage-and-ratio-word-problems/Percentage-and-ratio-word-problems.faq.question.1204488.html</a>
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